1. Field of the Invention
The present invention relates to further improvements with respect to models and algorithms to simulate and analyze ink ejection from a piezoelectric print head. More particularly, this invention recognizes and solves an instability that occurs as the head of a droplet reaches the end of the solution domain during simulation. A “consistent back pressure” formulation is introduced into the simulation models and algorithms to eliminate the instability. The improved simulation models and algorithms may be embodied in software, hardware or combination thereof and may be implemented on a computer or other processor-controlled device.
2. Description of the Related Art
Results of computational fluid dynamics (CFD) ink-jet simulation have been very useful in the design of piezoelectric ink-jet print heads. FIG. 1 shows how a practical ink-jet simulation may be carried out. An analytical tool such as an equivalent circuit 11 receives as an input the dynamic voltage to be applied to the piezoelectric PZT actuator and simulates the ink behavior under the influence of the ink cartridge, supply channel, vibration plate, and PZT actuator. That is, from the input voltage and an ink flow rate, the equivalent circuit 11 calculates an inflow pressure that drives the CFD code 12. The CFD code 12 then solves the governing partial differential equations, i.e., the incompressible Navier-Stokes equations for two-phase flows, for fluid velocity, pressure and interface position, and feeds back the ink flow rate to the equivalent circuit. The sequence is repeated as long as needed.